The optical conductivity of free carriers in GaAs

Abstract

The optical conductivity of free electrons in polar semiconducting compounds has recently been calculated by use of a generalized Boltzmann equation derived from the equation of motion of the quantum density matrix. This reduces to the quasi-classical Boltzmann transport equation in the low frequency limit: the optical conductivity thus obtained spans a spectral range from around 30cm −1 to 1.2 × 10 4 cm −1 in GaAs. In this paper, the optical conductivity is calculated for GaAs as a function of carrier concentration in terms of a frequency dependent relaxation time which reduces to the usual relaxation time in the limit of low frequencies and an elastic scattering mechanism. The low frequency limit of the relaxation time is used to estimate the mobility as a function of carrier concentration. The frequency dependent relaxation time is given for GaAs at 298 K over the spectral region from 45 cm −1 to 2.3 × 10 3 cm −1 for carrier concentrations from 3.4 × 10 15 cm −3 to 8.7 × 10 18 cm −3.